Word problem

Question

a large snowplow can clear a parking lot in 4 hours. A small snowplow needs more time to clear the lot. Working together, they can clear the lot in 3 hours. How long would it take the small plow to clear the lot by itself? 

Answer 1

Nina, let's let s = the time of the smaller plow.

 

In one hour, the larger can do 1/4 of a lot, right?  Then, the smaller plow can do 1/s of a lot.

 

Working together to do 1 lot, we multiply their rates by the time.

 

1/4(3) + 1/s(3) = 1

3/4 + 3/s = 1

 

The common denominator is 4s, so...

 

3s/4s + 12/4s = 1

 

With a common denominator, we can now combine the numerators...

 

(3s+12)/4s = 1

 

We multiply both sides by 4s...

 

3s + 12 = 4s

        12 = s

 

So, it would take the smaller plow 12 hours to clear the lot by itself.  Waaaay slower!